Question 282505
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Just so the explanation doesn't look quite so ugly with all of those capital letters that make you keep referring back to the diagram, I'm going to let *[tex \Large x] represent the value of the measure of AB.  Likewise, the value of the measure of BC will be *[tex \Large y] and the value of the measure of CD will be CD.  The value of the measure of AD is given as 9.


We are given that *[tex \Large y\ =\ z] and we can see that AD is the sum of *[tex \Large x\ +\ y\ +\ z], so we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ +\ z\ =\ x\ +\ 2y\ = 9]


Also, we are given that *[tex \Large x\ -\ 1\ =\ y\ +\ z\ =\ 2y]


which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 2y\ =\ 1]


Solving this little system we get


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ =\ 10]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 5]


And knowing that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 1\ =\ 2y] we can substitute


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5\ -\ 1\ =\ 2y\ \Rightarrow\ y\ =\ 4]


So AB = 5, BC = 4, and CD = 4, and BD must be 8.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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